
The first result we present in this framework is due to [1]}.
Authors have proved the following theorem using the ideas how to detect linearly independent column provided in the paper [2]}.

Let M be an underlying \(n_1 \times n_2\)  sized matrix of rank\(-r\)  and column space coherence \(\mu _0\) .
Assuming that \(\Omega \)  provided above in the algorithm satisfies the condition that its size is lower bounded by \(\Vert  \Omega \Vert  > 36 r^{3/2} \mu _0 \log { \frac{r}{\epsilon }}\)  then the algorithm successfully exactly recovers the underlying matrix \(M\)  with probability of   \(1-\epsilon \) .
